For example, [1]} has suggested that the variation of the carbon mass fraction in the C+O WD (C/O), or the variation of the initial WD mass, causes the diversity of SN Ia brightnesses (see [2]}). Similarly, [3]} argue that C/O and progenitor metallicity, Z, are intimately related for a fixed WD mass, and particularly for high metallicities given that it results in lower 3\(\alpha \)  burning rates plus an increased reduction of carbon via \(^{12}\) C(\(\alpha \) ,\(\gamma \) )\(^{16}\) O.
For Z \(>\)  Z\(_{\odot }\)  (\(\sim \) 0.02), [3]} find that both C/O and Z have an approximately equal influence on \(^{56}\) Ni production since, for a given WD mass, high progenitor metallicities (a greater abundance of species heavier than oxygen) and low C/O abundances (low carbon-rich fuel assuming a single-degenerate scenario) result in a low \(^{56}\) Ni yield and subsequently dimmer SN Ia. For near solar metallicities or less, the carbon mass fraction plays a dominant role in \(^{56}\) Ni production [5]}. This then suggests that the average C/O ratio in the final state of the progenitor is an important physical cause, in addition to metallicity, for the observed width-luminosity relationship (WLRA WLR is followed when a SN Ia has a proportionately broader light curve for its intrinsic brightness at maximum light [6]}. [7]} later extended this correlation by incorporating measurement of the extinction via late time B \(-\)  V color measurements and B \(-\)  V and V \(-\)  I measurements at maximum light (see also [8]}, [9]}). Because lights curves of faint SN Ia evolve promptly before 15 days post-maximum light, light curve shape measurements are better suited for evaluating the light curve “stretch” [10]}.) of normal SN Ia light curves [11]}, [5]}, [1]}, [14]}, [3]}.
